Author: Gerrit Reubold
Date: 12:40:07 09/27/02
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On September 27, 2002 at 15:04:26, Uri Blass wrote: >On September 27, 2002 at 14:40:09, Gerrit Reubold wrote: > >>Uri, >> >>I think your model of the game is not a model of the situation which I am >>discussing. >> >>Suppose you and me are playing the following game (f.ex. by email). >> >>1. I, the host, take an empty chessboard and put a single king one one of the >>squares. Trust me that I don't cheat. You send me your guess which square this >>might be. >> >>2. I assume you, the candidate, guess it is a1. >> >>3. I give you a hint: >>The square is not one of >> b1 c1 d1 e1 f1 g1 h1 >>a2 b2 c2 d2 e2 f2 g2 h2 >>a3 b3 c3 d3 e3 f3 g3 h3 >>a4 b4 c4 d4 e4 f4 g4 h4 >>a5 b5 c5 d5 e5 f5 h5 >>a6 b6 c6 d6 e6 f6 g6 h6 >>a7 b7 c7 d7 e7 f7 g7 h7 >>a8 b8 c8 d8 e8 f8 g8 h8 >> >>(Note that it is no difference if I suddenly forgot on which square the king >>stands, I decide to look only on the given 62 squares and, surprise, all of them >>are empty.) > >It is important if you know where the king is. No. > >Suppose for the discussion that you also do not know where the king is >so you always expose all the squares except a1 g5 after >I choose a1. No. I look at 62 random squares, excluding a1. > >Suppose that we start to play 64000 games(most of them are >not played because you discover the king >in one of the 62 squares). No. We play only this single game. We might play again and my hint will likely be different, maybe all squares except a1 and f8. Do you think it is a difference whether I forgot where the king is (I would have told you "game over" if I accidently looked at a square with the king on it) or whether I know the square of the king. > >Suppose that the king is in every suqare in 1000 cases > >Do you agree that it is logical to expect it? > >In 62000 games the king is not in a1 and not in g5 and the game >is not played. > >Do you agree? > >in 1000 games the king is in a1 and I win by not switching. >do you agree? > >In 1000 games the king is in g5 and I lose if I do not switch >Do you agree? > >in 1000 games out of 2000 games that are played I win by not switching >Do you agree? > >It means that the probability for me to win by not switching is exactly 1/2. > >Do you agree? > >Uri
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